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(C) In the argument of the sine function,$\frac{2 \pi nt}{\lambda}$ must be dimensionless. Since $2\pi$ is dimensionless,the dimensions of $\frac{nt}{

Vedclass · Accepted Answer

The dimensions of $n/\lambda$ are $[T^{-1}]$.

Vedclass · Answer

(C) In the argument of the sine function,$\frac{2 \pi nt}{\lambda}$ must be dimensionless. Since $2\pi$ is dimensionless,the dimensions of $\frac{nt}{\lambda}$ must be $[M^0 L^0 T^0]$.This implies $[nt] = [\lambda] = [L]$. Thus,option $A$ is correct.Given $[nt] = [L]$ and $[t] = [T]$,we have $[n] = [L/T] = [LT^{-1}]$. Thus,option $B$ is correct.For the cosine function,$\frac{2 \pi x}{\lambda}$ must be dimensionless,so $[x] = [\lambda] = [L]$. Thus,option $D$ is correct.Now,consider the dimensions of $n/\lambda$. Since $[n] = [LT^{-1}]$ and $[\lambda] = [L]$,we have $[n/\lambda] = [LT^{-1}] / [L] = [T^{-1}]$.Option $C$ states the dimensions are $[T]$,which is incorrect. Therefore,option $C$ is the correct answer.

The equation of a stationary wave is given by $y = 2a \sin \left( \frac{2 \pi nt}{\lambda} \right) \cos \left( \frac{2 \pi x}{\lambda} \right)$. Which of the following statements is $NOT$ correct?

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